Write a recurrence equation for the number of comparisons T(n) needed to process MergeSort on an input array of size n. Answer:
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- Dr. Sponge thinks it's too hard to implement Merge. So, he wants to replace Merge with Insertion Sort (yes, the insertion sort you learned in class). The following is the pseudo-code of the new Merge-Sort, Merge-Sort(p, r) 1. if p == r return 2. q = floor of (p+ r) / 2 3. Merge-Sort(p, q) 4. Merge-Sort(q+1, r) 5. Insertion-Sort(p, r) Give the recurrence for the running time of this new Merge-Sort and solve it. We let T(n) denote the running time when input array has n elements. By solving the recurrence (no need to show how you solved it), we obtain T(n) =A. Can you draw the animation of Merge sort: given an unsorted array of size 10, show the divide andconquer techniqueb. What is Running time for Merge Sort: O(nlogn) such that n is the size of thearray: Reference code attachedLet A be an array, where each of the n elements is a randomly chosen digit between 0 and 9. For example, if n = 12, this array could be A = [3,5,1,0,5,7,9,2,2,8,8,6]. Determine whether Counting Sort or Merge Sort sorts this array faster.
- Write a program to compute the exact value of the number of array accesses usedby top-down mergesort and by bottom-up mergesort. Use your program to plot the values for N from 1 to 512, and to compare the exact values with the upper bound 6N lg N.Mergesort is a method that takes an integer array and returns a sorted copy of the same array. It first sorts the left half of the input array, then the right half of the input array, and finally merges the two sorted halves together into a sorted version of the input array. Implement the mergesort method public static int[] mergesort(int[] arr) { return new int[] {-1}; } *must be in this layout and done in javaCreate a merge-sort multithread.A is an array, and p and q are array indexes used to sort the sub-array A[p..r]. B is a subarray that will be filled by the sort. A p-merge-sort(A,p,r,B,s) call sorts items from A[p..r] and places them in B[s..s+r-p].
- an array of integers nums sorted in ascending order, find the startingand ending position of a given target value. If the target is not found in thearray, return [-1, -1]. For example:Input: nums = [5,7,7,8,8,8,10], target = 8Output: [3,5]Input: nums = [5,7,7,8,8,8,10], target = 11Output: [-1,-1].Please do not give solution in image formate thanku.